Because infectious diseases are transmitted from person to person, our understanding of disease transmission and prevention are rooted in a theory of population transmission dynamics. The epidemiology of sexually transmitted infections (STI) like HIV -- how quickly they spread and who is infected -- is driven by the network of person-to-person contacts. Early epidemiological studies and mathematical models of this process provided a number of insights that led to changes in STI control strategies during the 1980s. With the advent of HIV, however, new challenges have emerged. Like other incurable infections, HIV has the potential to spread very broadly in a population under the right circumstances. This makes the "core group" concept from the 1980s somewhat less effective for HIV prevention. Much work has been done during the last 15 years to identify which aspects of the partnership network structure matter for the spread of HIV, and to collect data on partnership networks in many populations. Simulation studies have played a crucial role in this effort, by identifying the type of network structures that have large impacts on transmission dynamics. The confluence of data, theory, and methods has created a clear agenda for quantifying the influence of networks on HIV transmission risks. While many of the pieces of the emerging research program are now in place, there is a wide gulf between the network data and the current simulation modeling frameworks. Simulations typically create network effects indirectly, by varying parameters of some convenient function to produce a change in simulated networks. The observable network measures are thus outcomes of the model, rather than inputs. While this strategy has been very useful for orienting initial research, it has hamstrung our ability to evaluate the empirical transmission risk in observed networks. We propose a solution here that is based on statistical models for random graphs: it can be used to estimate network parameters from data, and then simulate networks with those properties. Specifically, we propose to: (1) develop random graph models for estimating network parameters and simulating evolving networks, with epidemiologically relevant formal tests for goodness-of-fit. Both the estimation and simulation methods will be based on a common Markov Chain Monte Carlo (MCMC) algorithm, which will enable researchers for the first time to simulate networks that have the same statistical properties as those observed in real data. (2) Use these methods to identify the network structures that matter most for the transmission of HIV. In particular, we will examine the independent and joint effects of needle sharing and sexual transmission, and we will test whether assortative mixing and concurrency determine the bulk of the transmission potential in a network. The methods developed will provide a systematic empirical basis for individual-level prevention strategies that focus on partnership interventions. It will enable public health professionals to identify population-level prevention strategies that make a network less vulnerable to spread. Moreover, it will identify the type of network data needed to inform such efforts.